A two-dimensional two-scale slice model has been developed to predict the
microstructure evolution in the solidifying strand with an arbitrary cross section geometry during
continuous casting of steel. The enthalpy equation is solved at the macro level by using meshless
local radial basis function collocation method (LRBFCM) based on multiquadrics for spatial
discretization and explicit Euler scheme for temporal discretization. The temperature and the solid
fraction in computational nodes are calculated by using a continuum model formulation while the
lever rule is used as the supplementary microsegregation relation. The temperature field is
interpolated to the micro level by using LRBFCM. At the micro level, the normal distribution and
Kurz-Giovanola-Trivedi model are proposed to determine temperature dependent nucleation rate and
grain growth velocity, respectively. Meshless point-automata algorithm is applied to implement
nucleation and grain growth equations. Several examples of computations of the strand with
different cross-sections are
shown
